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SLOGICA
2011

Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics

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Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics
Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We show that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in our strong sense. This applies to practically all three-valued paraconsistent logics that have been considered in the literature, including a large family of logics which were developed by da Costa’s school. Then we show that in contrast, paraconsistent logics based on three-valued properly non-deterministic matrices are not maximal, except for a few special cases (which are fully characterized). However, these non-deterministic matrices are useful for representing in a clear and concise w...
Ofer Arieli, Arnon Avron, Anna Zamansky
Added 15 May 2011
Updated 15 May 2011
Type Journal
Year 2011
Where SLOGICA
Authors Ofer Arieli, Arnon Avron, Anna Zamansky
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